Research on controlled synchronization transmission with one roller in a vibrating system driven by two actuators

The theory of the vibrating synchronization transmission belongs to a branch of nonlinear vibration. It is widely applied to the vibro-crusher in engineering. Owing to the dynamical characteristics constraints of the vibrating system, the two actuators of the vibratory crusher should keep a sufficient distance to realize the vibration synchronization transmission. Consequently, the vibratory crusher is hard to be applied in some mechanical systems with limited space because of the difficulty in miniaturization. To solve the above problem, this article addresses the problem of the structure miniaturization of the vibration crusher by controlling the actuators. The electromechanical coupling dynamics model is first established with Lagrange’s partial differential equations. The synchronization condition of the vibrating system is derived, and its stability condition is acquired through the Routh-Hurwitz stability criterion. In addition, the dynamic character is analyzed. For the dynamic conditions beyond the range of the synchronization transmission capacity, a proportional-integral-derivative (PID) controlling method is used for realizing the controlled synchronization transmission based on a control strategy of slave-master. Combined with the numerical results of the simulations, it is indicated that the proposed controlled synchronization transmission method is feasible and effective. The two actuators can realize the result of zero-phase-difference based on the synchronization motion. The roller can realize the circular motion with attaching to the inner wall. Finally, the vibro-crusher can realize the miniaturized structure design without affecting its function. The proposed method provides a valuable reference to the vibrating transmission equipment in engineering.